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- Homework Statement
- One end of a string is attached to a ball, with the other end held by a student such that the ball is swung in a horizontal circular path of radius R at a constant tangential speed. At a later time, the tension force exerted on the ball remains constant, but the length of the string is decreased to R/4. What is the new tangential speed of the ball?

- Relevant Equations
- ##F_c = \frac {mv^2} R##

The answer key states that the new tangential speed is half the original speed. However, this isn't correct right? It should double.

My proof:

##F_c = \frac {mv^2} R##

##F_c = F_t##

##\frac {mv^2} {\frac R 4} = \frac {m(2v)^2} R## If centripetal force were to stay constant.

As such, tangential velocity should double right? It should not half?

My proof:

##F_c = \frac {mv^2} R##

##F_c = F_t##

##\frac {mv^2} {\frac R 4} = \frac {m(2v)^2} R## If centripetal force were to stay constant.

As such, tangential velocity should double right? It should not half?